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Maps, sheaves, and K3 surfaces

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 نشر من قبل Rahul Pandharipande
 تاريخ النشر 2008
  مجال البحث
والبحث باللغة English
 تأليف R. Pandharipande




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The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New results and conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The recent proof of the Yau-Zaslow conjecture is surveyed. The paper accompanies my lecture at the Clay research conference in Cambridge, MA in May 2008.



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